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Full text of "Scientific Papers - Vi"

434
ON THE DISPERSAL OF LIGHT BY A DIELECTRIC CYLINDER.
[Philosophical Magazine, Vol. xxxvi. pp. 365—376, 1918.]
THE problem of the incidence of plane electric waves on an insulating dielectric cylinder was treated by me as long ago as 1881*. Further investigations upon the same subject have been published by Seitzf and by Ignatowski]: who corrects some of Seitz's results. Neither of these authors appears to have been acquainted with my much earlier work. The purpose of the present paper is little more than numerical calculations from the expressions formerly given, but in order to make them intelligible it will be well to quote what was then said. The notation is for the most part Maxwell's.
"We will now return to the two-dimension problem with the view of determining the disturbance resulting from the impact of plane waves upon a cylindrical obstacle whose axis is parallel to the plane of the waves. There are, as in the problem of reflection from plane surfaces, two principal cases— (1) when the electric displacements are parallel to the axis of the cylinder taken as axis of z, (2) when the electric displacements are perpendicular to this direction.
"Case 1. [From the general equation with conductivity (0) zero and magnetic permeability (/JL) constant],
or if, as before, k = 27T/A,,
/d*      d2     7,\ h
I______L______L  JfZ I  ___
in which k is constant in each medium, but changes as we pass from one medium to another.   From (2) we see that the problem now before us is
* Phil. Mag. Vol. xu. p. 81 (1881); Scientific Papers, Vol. i. p. 533. t Ann. d. Phijsik, Vol. xvr. p. 746 (1905); Vol. xrx. p. 554 (1906). J Ann. d. Physik, Vol. xvm. p. 495 (1905).
§ The numbering of the equations is changed,    h is the component of electric displacement parallel to z, K the specific inductive capacity, and X the wave-length.too violently, the fluid refuses to follow the walls, eddies result, and mechanical energy is lost by fluid friction. According to W. Froude's generally accepted view, the explanation is to be sought in the loss of velocity near the walls in consequence of fluid friction, which is such that the fluid